ESTIMATION OF EVAPOURATION LOSS ON BOARD TANKERS

Application of Bernoulli’s theorem from Fluid Mechanics

ESTIMATION OF EVAPOURATION LOSS ON BOARD TANKERS

“ AN EQUATION FOR ME HAS NO MEANING, UNLESS IT REPRESENTS A THOUGHT OF GOD”

--GIFTED MATHEMATICIAN OF THIS COUNTRYMR. SRINIVASA RAMANUJAN (1887-1920)--

Few Facts on Srinivasa Ramanujan

• He had no formal qualification prior to going to UK for higher studies. He passed only F.A (equivalent to Intermediate or PUC)

• At the age of 12, he mastered Advanced Trignometry by S.L. Loney

• Poverty stricken Ramanujan, could not afford to purchase paper but used to work out problems in slate and write end-results in his note book.

Facts on Srinivasa Ramanujan

• He got employed in a marine related industry. Yes Madras Port Trust as a Clerk.

• He went to Trinity College, UK for higher studies in Maths.

• He was the second Indian to have been elected as Fellow of Royal Society and first Indian to have been elected as Fellow of Trinity College, Cambridge.

• Prof. G.H. Hardy- Ramanujan’s Guide, when asked about his contribution to Mathematics

Few Facts on Srinivasa Ramanujan

• Used to say ”Introducing Ramanujan to western world was his greatest contribution”

• That talks about the fame of this mathematician.

• His birth day 22 December is declared by Indian Govt. as National Mathematic Day.

• With these words on that gifted mathematician and with a thought of God let me commence my presentation.

INTRODUCTION• THE SPEAKER STARTED OFF HIS CAREER WITH SURVEYING OF

BULK PETROLEUM CRUDE OIL TANKERS.• AFTER COMPLETION OF SURVEY AND SHORE OUT TURN AND

REASONS FOR PROVIDING MISMATCH BETWEEN SHIP’S QTY AND SHORE QTY USED TO BE MIND BOGGLING.

• REASONS FOR SHORTAGE NORMALLY ATTRIBUTED IN GENERAL TO NORAML HANDLING LOSSES LIKE LEAKAGE, EVAPOURATION, ROB ETC.

• HERE IS AN ATTEMPT TO QUANTIFY EVAPOURATION LOSS, AS NOW ADAYS TANKERS ARE PROVIDED WITH LOT OF AUTOMATION/INSTRUMENTATION TO RECORD NECESSARY DATA.

Evaporation loss

Problem under study

• Let us assume a vessel containing a certain fluid at some pressure.

• The vessel contains an automated valve which opens itself to let out fluid to avoid excess pressure to build up in the vessel.

• Lets say the valve opens for a certain time intervals to release pressure.

• The aim of the problem is to estimate the volume of fluid that came out of the vessel

Formulation of Problem

Inputs for the problem:- Initial Pressure in the vessel- Cross-sectional area of pipe- Time duration for which valve is openedAll other material properties and physical constants are assumed appropriately.

Methodology

• With these available inputs, the problem is solved with the application of Bernoulli’s theorem.

• Many of you are Engineers and familiar with Fluid Dynamics and Bernoulli’s theorem. Still let me give a brief note about the same.

Theory

All fluids possess energy (a.k.a. head) in three forms :-– Pressure Energy– Flow Energy– Gravitational Energy

And the total energy of a fluid is sum of all these three energy forms.

Theory

• According to Bernoulli’s theorem, for a steady, incompressible fluid flow, the total fluid energy is constant throughout the flow.

• In other words, the sum of all forms of fluid energy at one point of flow is equals sum of all energy forms at another point of fluid flow.

Theory

TheoryMathematically, this is written as shown below,

p1/ρ + v12/2g + z1= p2/ρ + v2

2/2g + z2

wherep1,p2 = fluid pressure at point 1 & 2

v1,v2 = flow velocity at point 1 & 2 z1,z2 = height/level of fluid at point 1 & 2

ρ is fluid density & g is acceleration due to gravity

Theory

• Discharge is defined as the volume of fluid flow per unit time which is therefore the ratio of volume to time.

• Mathematically,• Discharge, Q = V/t ; V-Volume; t-Time

= A x l/t ; V=Area (A) x length (l)

= A x v ; v-flow velocity

Applying the theory in current problem

The above theories may be applied in the problem under study but subject to following assumptions.

• The flow is steady i.e. the flow parameters are constant with time.

• The fluid is incompressible i.e. the fluid has constant density at a given temperature.

• The temperature of flowing fluid remains constant.

Case study

There is a vessel containing a gas at a pressure of 2bar. The relief valve which is fit on a pipe of 30mm diameter opens for 40seconds. What volume of gas has escaped? Assume the pipe to be horizontal or vertical and flow to be steady & incompressible.

Inputs: p1 = 2bar = 202650 Pa ;

p2 = patm = 1bar = 101325 Pa ; v1 = 0 ; z1 = z2

ρ = 500 kg/m3 ; g = 9.8 m/s2 ; t = 40 s

Case study

Applying Bernoulli’s theorem, p1/ρ + v1

2/2g + z1 = p2/ρ + v22/2g + z2

Substituting it in the above theorem and solving it, we get v2 = 61.58 m/sNow using the relation, Q = Av (A=πd2/4)

Q = 0.0435 m3/s = Volume / timeBut time of flow, t = 10s

Volume, V = Qt = 0.435 m3 = 435 litres

Inference

• The above methodology does not describe the actual volume of gas flowing out because it assumes steady flow.

• Due to this assumption, the final gas volume will be increased than the actual.

• However, this can account for the maximum amount of vapor that has flown out.

Limitation

• As Crude oil tankers now a days are fitted with Crude Oil Washing system using flu gas as inert gas, it is very difficult to isolate and estimate how much hydrocarbon contents lost.

Insurer’s point of view.

• As evaporation loss is inherent vice or nature of any Petroleum product, quantity so estimated may be excluded as per ICC-A General Exclusion Clause.

• But in Indian scenario, since Petroleum Crude and products are invariably insured for TLO (Total Loss Only), this is only an academic interest.

ACKNOWLEDGEMENT

• SPEAKER COVEYS THANKS TO MR. T.S.SADAGOAPAN – A RESEARCH SCHOLAR UNDERGOING M.S IN MECHANICAL ENGINNERING IN IIT (MADRAS) FOR TECHNICAL INPUTS.

• SPEAKER ALSO CONVEYS THANKS TO CAPT. S.P. ANAND AND MR. P.SRIDHARAN OF HENDERSON INTERNATIONAL FOR THEIR ENCOURAGEMENT & SUPPORT.